机器学习实战5：k-means聚类：二分k均值聚类+地理位置聚簇实例

　　k-均值聚类是非监督学习的一种，输入必须指定聚簇中心个数k。k均值是基于相似度的聚类，为没有标签的一簇实例分为一类。

　　一 经典的k-均值聚类　　

　　思路：　　

　　1 随机创建k个质心（k必须指定，二维的很容易确定，可视化数据分布，直观确定即可）；

　　2 遍历数据集的每个实例，计算其到每个质心的相似度，这里也就是欧氏距离；把每个实例都分配到距离最近的质心的那一类，用一个二维数组数据结构保存，第一列是最近质心序号，第二列是距离；

　　3 根据二维数组保存的数据，重新计算每个聚簇新的质心；

　　4 迭代2 和 3，直到收敛，即质心不再变化；

from numpy import *

def loadDataSet(fileName):      #general function to parse tab -delimited floats
    dataMat = []                #assume last column is target value
    fr = open(fileName)
    for line in fr.readlines():
        curLine = line.strip().split('	')
        fltLine = map(float,curLine) #map all elements to float()
        dataMat.append(fltLine)
    return dataMat

def distEclud(vecA, vecB):
    return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB)

def randCent(dataSet, k):
    n = shape(dataSet)[1]
    centroids = mat(zeros((k,n)))#create centroid mat
    for j in range(n):#create random cluster centers, within bounds of each dimension
        minJ = min(dataSet[:,j]) 
        rangeJ = float(max(dataSet[:,j]) - minJ)
        centroids[:,j] = mat(minJ + rangeJ * random.rand(k,1))
    return centroids
    
def kMeans(dataSet, k, distMeas=distEclud, createCent=randCent):
    m = shape(dataSet)[0]
    clusterAssment = mat(zeros((m,2)))#create mat to assign data points 
                                      #to a centroid, also holds SE of each point
    centroids = createCent(dataSet, k)
    clusterChanged = True
    while clusterChanged:
        clusterChanged = False
        for i in range(m):#for each data point assign it to the closest centroid
            minDist = inf; minIndex = -1
            for j in range(k):
                distJI = distMeas(centroids[j,:],dataSet[i,:])
                if distJI < minDist:
                    minDist = distJI; minIndex = j
            if clusterAssment[i,0] != minIndex: clusterChanged = True
            clusterAssment[i,:] = minIndex,minDist**2
        print centroids
        for cent in range(k):#recalculate centroids
            ptsInClust = dataSet[nonzero(clusterAssment[:,0].A==cent)[0]]#get all the point in this cluster
            centroids[cent,:] = mean(ptsInClust, axis=0) #assign centroid to mean 
    return centroids, clusterAssment

　　经典的k均值聚类有很大的缺点就是很容易收敛到局部最优，为了避免这种局部最优，我们引入了二分k-均值算法。

　　二 二分k-均值聚类算法

　　二分k-均值聚类算法是基于经典k-均值算法实现的；里面调用经典k-均值（k=2），把一个聚簇分成两个，迭代到分成k个停止；

　　具体思路：

　　1 把整个数据集看成一个聚簇，计算质心；并用同样的数据结构二维数组保存每个实例到质心的距离；

　　2 对每一个聚簇进行2-均值聚类划分；

　　3 计算划分后的误差，选择所有被划分的聚簇中总误差最小的划分保存；

　　4 迭代2 和 3 直到聚簇数目达到k停止；

def biKmeans(dataSet, k, distMeas=distEclud):
    m = shape(dataSet)[0]
    clusterAssment = mat(zeros((m,2)))
    centroid0 = mean(dataSet, axis=0).tolist()[0]
    centList =[centroid0] #create a list with one centroid
    for j in range(m):#calc initial Error
        clusterAssment[j,1] = distMeas(mat(centroid0), dataSet[j,:])**2
    while (len(centList) < k):
        lowestSSE = inf
        for i in range(len(centList)):
            ptsInCurrCluster = dataSet[nonzero(clusterAssment[:,0].A==i)[0],:]#get the data points currently in cluster i
            centroidMat, splitClustAss = kMeans(ptsInCurrCluster, 2, distMeas)
            sseSplit = sum(splitClustAss[:,1])#compare the SSE to the currrent minimum
            sseNotSplit = sum(clusterAssment[nonzero(clusterAssment[:,0].A!=i)[0],1])
            print "sseSplit, and notSplit: ",sseSplit,'--',sseNotSplit
            if (sseSplit + sseNotSplit) < lowestSSE:
                bestCentToSplit = i
                bestNewCents = centroidMat
                bestClustAss = splitClustAss.copy()
                lowestSSE = sseSplit + sseNotSplit
        bestClustAss[nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList) #change 1 to 3,4, or whatever
        bestClustAss[nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit
        print 'the bestCentToSplit is: ',bestCentToSplit
        print 'the len of bestClustAss is: ', len(bestClustAss)
        centList[bestCentToSplit] = bestNewCents[0,:].tolist()[0]#replace a centroid with two best centroids 
        centList.append(bestNewCents[1,:].tolist()[0])
        clusterAssment[nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:]= bestClustAss#reassign new clusters, and SSE
    return mat(centList), clusterAssment

　　三 地理位置聚簇实例

　　地理位置的经纬度正好是二维的，可以可视化出来，所以很适合聚类算法确定质心个数k值；值得注意的是，球面计算距离，不能简单的用欧式距离，而需要用球面距离公式，见函数distSLC；

　　代码的含义给定n个俱乐部地址名称，然后使用urllib包，调用yahoo地图的API返回经纬度，调用我们上面实现的k均值聚类算法，找到聚簇的中心，最后利用matplotlib工具可视化出来；

import urllib
import json
def geoGrab(stAddress, city):
    apiStem = 'http://where.yahooapis.com/geocode?'  #create a dict and constants for the goecoder
    params = {}
    params['flags'] = 'J'#JSON return type
    params['appid'] = 'aaa0VN6k'
    params['location'] = '%s %s' % (stAddress, city)
    url_params = urllib.urlencode(params)
    yahooApi = apiStem + url_params      #print url_params
    print yahooApi
    c=urllib.urlopen(yahooApi)
    return json.loads(c.read())

from time import sleep
def massPlaceFind(fileName):
    fw = open('places.txt', 'w')
    for line in open(fileName).readlines():
        line = line.strip()
        lineArr = line.split('	')
        retDict = geoGrab(lineArr[1], lineArr[2])
        if retDict['ResultSet']['Error'] == 0:
            lat = float(retDict['ResultSet']['Results'][0]['latitude'])
            lng = float(retDict['ResultSet']['Results'][0]['longitude'])
            print "%s	%f	%f" % (lineArr[0], lat, lng)
            fw.write('%s	%f	%f
' % (line, lat, lng))
        else: print "error fetching"
        sleep(1)
    fw.close()
    
def distSLC(vecA, vecB):#Spherical Law of Cosines
    a = sin(vecA[0,1]*pi/180) * sin(vecB[0,1]*pi/180)
    b = cos(vecA[0,1]*pi/180) * cos(vecB[0,1]*pi/180) * 
                      cos(pi * (vecB[0,0]-vecA[0,0]) /180)
    return arccos(a + b)*6371.0 #pi is imported with numpy

import matplotlib
import matplotlib.pyplot as plt
def clusterClubs(numClust=5):
    datList = []
    for line in open('places.txt').readlines():
        lineArr = line.split('	')
        datList.append([float(lineArr[4]), float(lineArr[3])])
    datMat = mat(datList)
    myCentroids, clustAssing = biKmeans(datMat, numClust, distMeas=distSLC)
    fig = plt.figure()
    rect=[0.1,0.1,0.8,0.8]
    scatterMarkers=['s', 'o', '^', '8', 'p', 
                    'd', 'v', 'h', '>', '<']
    axprops = dict(xticks=[], yticks=[])
    ax0=fig.add_axes(rect, label='ax0', **axprops)
    imgP = plt.imread('Portland.png')
    ax0.imshow(imgP)
    ax1=fig.add_axes(rect, label='ax1', frameon=False)
    for i in range(numClust):
        ptsInCurrCluster = datMat[nonzero(clustAssing[:,0].A==i)[0],:]
        markerStyle = scatterMarkers[i % len(scatterMarkers)]
        ax1.scatter(ptsInCurrCluster[:,0].flatten().A[0], ptsInCurrCluster[:,1].flatten().A[0], marker=markerStyle, s=90)
    ax1.scatter(myCentroids[:,0].flatten().A[0], myCentroids[:,1].flatten().A[0], marker='+', s=300)
    plt.show()

　　四 总结

　　优点：易实现；

　　缺点：可能收敛到局部最小值，在大数据集上收敛较慢；

　　适用数据类型：数值型；